Charbonneau, P; Corwin, EI; Parisi, G; Poncet, A; Zamponi, F, *Universal Non-Debye Scaling in the Density of States of Amorphous Solids.*,
Physical Review Letters, vol. 117 no. 4
(July, 2016),
pp. 045503 [doi] .
**Abstract:**

*At the jamming transition, amorphous packings are known to display anomalous vibrational modes with a density of states (DOS) that remains constant at low frequency. The scaling of the DOS at higher packing fractions remains, however, unclear. One might expect to find a simple Debye scaling, but recent results from effective medium theory and the exact solution of mean-field models both predict an anomalous, non-Debye scaling. Being mean-field in nature, however, these solutions are only strictly valid in the limit of infinite spatial dimension, and it is unclear what value they have for finite-dimensional systems. Here, we study packings of soft spheres in dimensions 3 through 7 and find, away from jamming, a universal non-Debye scaling of the DOS that is consistent with the mean-field predictions. We also consider how the soft mode participation ratio evolves as dimension increases.*